Photosynthetic microorganisms are endowed with the unique ability to utilize light energy to convert inorganic carbon into biomass, offering an opportunity to use metabolically-designed cyanobacteria to synthesize biofuels and high value chemicals for societal benefits. Farnesene, a C15-hydrocarbon, has a similar energy density to diesel and jet fuels, and is a sought-after compound for large-scale production using engineered cyanobacteria. Here, we report the photosynthetic production of farnesene by the filamentous nitrogen-fixing cyanobacterium Anabaena sp. PCC 7120 using CO2, water, and light. A codon-optimized farnesene synthase (FaS) gene from Norway spruce was expressed in the cyanobacterium, giving it the ability to synthesize farnesene using its endogenous MEP pathway. Volatized farnesene was emitted from the engineered strain into the flask headspace, allowing for quick separation of the target compound from the culture biomass. Thus, the engineered Anabaena serves as a solar-driven, living cellular factory for continuous farnesene production. Total farnesene yield was measured to be 305.4±17.7 µg·L-1 during a 15-day production trial, with a maximum productivity of 69.1±1.8 µg·L-1·O.D.-1·d-1. We envision the use of metabolically-engineered cyanobacteria as a biosolar factory for production of a wide range of biofuels and commodity chemicals.